Correlation energy types

The acronym SEC refers to the case where the reference wave function is of the MCSCF type and tire correlation energy is calculated by an MR-CISD procedure. When the reference is a single determinant (HE) the SAC nomenclature is used. In the latter case the correlation energy may be calculated for example by MP2, MP4 or CCSD, producing acronyms like MP2-SAC, MP4-SAC and CCSD-SAC. In the SEC/SAC procedure the scale factor F is assumed constant over the whole surface. If more than one dissociation channel is important, a suitable average F may be used. 

The correlation energy is expected to have an inverse power dependence once the basis set reaches a sufficient (large) size. Extrapolating the correlation contribution for n = 3-5(6) with a function of the type A + B n + I) yields the cc-pVooZ values in Table 11.8. The extrapolated CCSD(T) energy is —76.376 a.u., yielding a valence correlation energy of —0.308 a.u. 

A b initio calculations may be applied to isomerization reactions or "bond separation reactions in which the bond type persists and correlation energies are unlikely to alter. For example,... 

The operation of Eq. (3.3) is illustrated by the results given in Table 2 out of 48 molecules of the cc-pVTZ set. They are listed in order of increasing correlation energy. The first column of the table lists the molecule. The next 6 columns show how many orbitals and orbital pairs of the various types are in each molecule, i.e. the numbers Nl, Nb, Nu, Nlb etc. The seventh column lists the CCSD(T)/triple-zeta correlation energy and the eight column lists the difference between the latter and the prediction by Eq. (3.3). The mean absolute deviation over the entire set of cc-pVTZ data set is 3.14 kcal/mol. For the 18 molecules of the CBS-limit data set it is found to be 1.57 kcal/mol. The maximum absolute deviations for the two data sets are 11.29 kcal/mol and 4.64 kcal/mol, respectively. Since the errors do not increase with the size of the molecule, the errors in the estimates of the individual contributions must fluctuate randomly within any one molecule, i. e. there does not seem to exist a systematic error. The relative accuracy of the predictions increases thus with the size of the system. It should be kept in mind that CCSD(T) results can in fact deviate from full Cl results by amounts comparable to the mean absolute deviation associated with Eq. (3.3). 

By choosing a suitable isodesmic reaction, the heat of formation of the new species can be determined from the calculated value of the heat of reaction and the thermochemistry of the remaining species, which must also be known. This approach provides an empirical correction in the form of cancellation of correlation energy that accompany the formation and breakage of specific types of bonds. 

Ec = E c - Ex have been employed. On the one hand, LDA and GGA type correlation functionals have been used [14], However, the success of the LDA (and, to a lesser extent, also the GGA) partially depends on an error cancellation between the exchange and correlation contributions, which is lost as soon as the exact Ex is used. On the other hand, the semiempirical orbital-dependent Colle-Salvetti functional [22] has been investigated [15]. Although the corresponding atomic correlation energies compare well [15] with the exact data extracted from experiment [23], the Colle-Salvetti correlation potential deviates substantially from the exact t)c = 8Ecl5n [24] in the case of closed subshell atoms [25]. 

Figures 2 and 3 plot the valence correlation energies of Ne and FH obtained by various combinations of the CC or CC-R12 methods (using Ten-no s Slater-type correlation function) and basis sets (see ref. 35 for details). These figures are the stunning illustration of the extremely rapid convergence of correlation energies...

The aim of this paper is ascertain whether it is possible to determine the ground state second-order correlation energy of the hydrogen molecule to sub-millihartree accuracy using a basis set containing only s-type Gaussian functions with exponents and distribution determined by an empirical, but physically motivated, procedure. 

It has been shown that the second order electron correlation energy for the ground state of the hydrogen molecule at its equilibriiun nuclear geometry can be described to an accmacy below the sub-milliHartree level using a distributed basis set of Gaussian basis subsets containing only s-type functions only. Each of the basis subsets are taken to be even-tempered sets. The distribution of the subsets is empirical but nevertheless physically motivated. 

As to the contributions of the ghost functions, those of s type are of the same behaviour than in the He2 dimer (see Table II, values are given for monomerl). The contributions of p functions, as expected, show a systematic trend it is to be emphasized that the contributions from monomerl in the SMOs for monomerl are usually higher than those from monomerl to monomerl. However, not so large difference can be noticed for the contributions in the corresponding CP-systems. These results also suggest that one cannot expect a similar correspondence for the correlation energy contributions in the SM- and CP-systems for the electron-donor and electron-acceptor monomers, respectively. 

Figure 1 Comparison of the convergence behaviour of the second order correlation energy component for the F anion with sequences of even-tempered Gaussian basis sets containing s- and p-type functions designed for the neutral F and Ne atoms with the behaviour of this component for the Ne atom. The cmrves are labelled as follows - (a) AE2 Ne [A e]) (b) AE2 F -, [iVe]) (c) AEtiF--, [F]).

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